Yes it will fire both, but it won't overdrive the DE like an HQI.
The ice cap ballast specs say "fires all 250w lamps", plus they are selling DE HQI lamps on their website.
http://209.204.76.225/index.htm
Overdriving to the point of not delivering 250, but using more like 280 to 300 watts.HQI ballasts dont overdrive DE bulbs. HQI ballasts drive DE bulbs to specification. Electronics underdrive DE bulbs, which can lead to shorter bulb life, as well as lower efficiency.